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A088431 Half of the (n+1)-st component of the continued fraction expansion of sum(k>=1,1/2^(2^k)). 5
2, 1, 2, 2, 3, 2, 1, 2, 3, 1, 2, 3, 2, 2, 1, 2, 3, 1, 2, 2, 3, 2, 1, 3, 2, 1, 2, 3, 2, 2, 1, 2, 3, 1, 2, 2, 3, 2, 1, 2, 3, 1, 2, 3, 2, 2, 1, 3, 2, 1, 2, 2, 3, 2, 1, 3, 2, 1, 2, 3, 2, 2, 1, 2, 3, 1, 2, 2, 3, 2, 1, 2, 3, 1, 2, 3, 2, 2, 1, 2, 3, 1, 2, 2, 3, 2, 1, 3, 2, 1, 2, 3, 2, 2, 1, 3, 2, 1, 2, 2, 3, 2, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

To construct the sequence use the rule : a(1)=2 then a(a(1)+a(2)+...+a(n)+1)=2 and fill in any undefined places with the sequence 1,3,1,3,1,3,1,3,1,3,1,3,.....

Contribution from Dimitri Hendriks, May 06 2010: (Start)

This sequence appears to be the sequence of run lengths of the regular paperfolding sequence A014577, i.e. the latter starts as follows: 2 zeros, 1 one, 2 zeros, 2 ones, etc. (End)

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192

FORMULA

a(n)= (1/2)*A007400(n+1); a(a(1)+a(2)+...+a(n)+1) = 2.

EXAMPLE

Example to illustrate the comment : a(a(1)+1)=a(3)=2 and a(2) is undefined. The rule forces a(2)=1. Next, a(a(1)+a(2)+1)=a(4)=2, a(a(1)+a(2)+a(3)+1)=a(6)=2 and a(5) is undefined. The rule forces now a(5)=3.

PROG

(Scheme) (define (A088431 n) (* 1/2 (A007400 (+ 1 n)))) ;; Code for A007400 given under that entry. - Antti Karttunen, Aug 12 2017

CROSSREFS

Cf. A007400, A014577, A088435, A092910.

Sequence in context: A134192 A284044 A126305 * A254661 A052304 A049874

Adjacent sequences:  A088428 A088429 A088430 * A088432 A088433 A088434

KEYWORD

nonn,changed

AUTHOR

Benoit Cloitre, Nov 08 2003

STATUS

approved

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Last modified August 20 17:20 EDT 2017. Contains 290837 sequences.